An axiomatic characterization of the quantile risk sharing rule pdf

In this video, I present the paper “An Axiomatic Characterization of the Quantile Risk-Sharing Rule” (SAJ 2025, https://www.tandfonline.com/doi/full/... ), which provides a rigorous foundation for a simple and practical loss allocation mechanism in heterogeneous insurance pools.

The main objective is to characterize the quantile risk-sharing rule through a clear set of axioms. The rule is designed for situations where participants have different marginal loss distributions, and where modelling or estimating the full dependence structure may be difficult or undesirable. The key idea is to map the realized aggregate loss to a common probability level using the comonotonic benchmark, and then allocate to each participant the quantile of their own marginal loss at that same probability level.

This talk explains:
the motivation for quantile-based allocations in risk sharing,
how the rule is constructed using the comonotonic counterpart,
an interpretation through an absolute-deviation optimization problem,
the main axiomatic characterization theorem (aggregate structure, dependence-free property, and stand-alone behavior for comonotonic pools),
and numerical illustrations highlighting state-dependent contributions, potential ranking reversals, and practical issues related to mass at zero in compound Poisson–type models.

This presentation is intended for actuarial science professors, PhD students, and researchers in insurance and risk management, with an emphasis on mathematical structure and implementation insight.

If you are interested in risk sharing, comonotonicity, allocation rules, and robust distribution-based methods, I hope you will find this talk useful.